In deriving the Eqs. (REF ) and (REF ) for \(n_s\) 
we have also considered that in WI that \(T_*/H_* \gg 1\)  (in
particular, \(T_*/H_* \gg 1\)  can be explicitly verified in the
examples to be considered in the next section). Finally, in the
regime \(T_*/H_* \ll 1\)  and \(Q_* \ll 1\)  we recover the cold inflation
standard result, \(n_s-1=-6 \epsilon _V + 2 \eta _V\) . We can note from
Eq. (REF ) that when \(c_{s*} \ll 1\) , in the absence of the
growing mode, \(G^{\prime }(Q) \rightarrow 0\) , we have that \(n_s-1 \propto - 1/Q\)  and
the spectral tilt will tend to be red-tilted for large \(Q\) . However,
in the presence of the growing mode, the last term in
Eq. (REF ) dominates at large \(Q\)  and it will tend to drive
the spectrum to be blue-tilted (for \(G^{\prime }(Q) > 0\) ). To better
illustrate the latter case, let us consider a few relevant WI
dissipation terms that have commonly been used in the literature,
namely, (a) the linear in the temperature dissipation
coefficient [1]}, with \(c=1,\, p=0\) ; (b) the
cubic in the temperature dissipation coefficient, with \(c=3,\,p=0\) 
(e.g., from Ref. [2]}) and (c) the dissipation
coefficient with \(c=3,\, p=-2\)  (see, e.g.,
Refs. [3]}, [4]}). For definiteness,
we will also consider the example of a primordial potential with a
quartic inflaton potential (\(n=2\) ), which has also been the primordial
potential mostly considered with these dissipation coefficients in
WI. We will also assume that the growing mode function is well
described by a polynomial function in the dissipation ratio \(Q\) , with
the leading term for \(Q\gg 1\)  of the form \(G(Q) \propto Q^\beta \) . Let
us see the results for each of these three cases separately.
